信用連結債券的價值主要取決於所連結資產池內的資產違約狀況，使得原始信用風險債券在到期時的本金償付受到其他債券的信用風險影響，因此如何準確且客觀的估計資產池內違約機率便一個很重要的課題，而過去文獻常以給定參數的方式，並且假設資產間的違約狀況彼此獨立下進行評價，對於聯合違約機率的捕捉並不明顯，因此本文延伸Factor Copula模型，建立信用連結債券之評價模型，該模型考慮了資產間的違約相關程度，以期達到符合市場的效果，同時配合統計之因素分析法，試圖找出影響商品價格背後的市場因子。 本研究利用延伸的評價模型以及Copula法，對實際商品做一訂價探討，結果發現，不管是使用樣本內或樣本外的資料去評價時，本研究的評價模型表現都優於Copula法，表示說評價時額外加入市場因子的考慮，對於評價是有正向的幫助；而在因子選取方面，我們選取18項因子後，經由因素分析共可萃取出三大類因素，藉由觀察期望價格與市場報價的均方根誤差，發現國家因素以及產業因素均對於商品價格有所影響，而全球因素對於商品不但沒有顯著影響，同時加入後還會使得計算出的商品期望價格更偏離市場報價，代表說並不是盲目的加入許多因子就能使得模型計算出的價格貼近市場報價，則是要視加入的因子對於資產的影響程度而定。 對於後續研究的建議：由於本研究的實證中存在一些假設，使得評價過程中並不完全符合現實市場現況，若能得到市場上的真實數據，或是改以隨機的方式來計算，相信結果會更貼近市場報價；同時，藉由選取不同的因子來評價，希望能找出國家因素、產業因素以外的其他影響因子，可助於我們更了解此項商品背後的影響因素，使得投資人能藉由觀察市場因子數據來判斷商品未來價格走勢。 / Value of the credit-linked notes depend on the pool of assets whether default or not, so the promised payoff of credit-linked notes is affected by other risky underlying assets. Therefore, how to estimate the probability of default asset pool accurately and objectively will be a very important issue. In the past literature, researchers usually use given parameters, and assume assets probability of default are independent from each other under valuation. Furthermore, it is not obvious to capture the joint probability of default. Thus, this article extends the Factor Copula Model to provide a new methodology of pricing credit-linked notes, which consider the default correlation between the extent of assets in order to achieve result in line with market and with Factor Analysis method added, trying to figure out the impact of commodity price factor behind the market. In the empirical analysis, pricing the actual commodity issued by LB Baden-Wuerttemberg using extend model and Copula model, we found that no matter choose in-the-sample or out-the-sample data to valuation, the models in this article are superior to Copula model by compare the root-mean-square deviation(RMSE). It means add the market factors into our valuation is beneficial. In terms of selection factors, we select eighteen factors prepared by Morgan Stanley Capital International, and three categories of factors may be extracted from Factor Analysis method. By observing RMSE, both national factors and industry factors will influence on the commodity, but world factors not only did not significantly impact on the commodity, but also add it to calculate the expected price further from the market price. Representative said not blind join the many factors can make the model to calculate the price close to the market price, it is a factor depending on the degree of influence of the added asset. For the suggestion of future research. The fact that the presence of empirical assumptions in this study, result in the evaluation process is not entirely realistic to market situation. We suggest to get the real data on the market or use random way to calculate, we believe that the outcome will be closer to the market price. Meanwhile, by selecting different factors to evaluate, trying to discover further factors which significantly impact on the commodity; it will help us better to understand the factors behind the commodity, so investors can predict commodity future prices by observing the market data.

1990年代中期信用衍生信商品開始發展，隨著時代變遷，演化出信用違約交換(Credit Default Swaps, CDS)、擔保債權憑證(Collateralized Debt Obligation, CDO)、合成型擔保債權憑證(Synthetic CDO)等商品，其可以分散風險的特性廣受歡迎，並且成為完備金融市場中重要的一環。在2007年金融海嘯中，信用衍生性商品扮演相當關鍵的角色，所以如何合理定價各類信用衍生性商品就變成相當重要的議題 以往在定價合成型擔保債權憑證時，多採取單因子結構模型來做為報酬函數的主要架構，並假設模型分配為常態分配、t分配、NIG分配等，但單因子結構模型的隱含相關係數具有波動性微笑現象，所以容易造成定價偏誤。 為了解決此問題，本文將引用常態分配假設與NIG分配假設下的隨機風險因子負荷模型(Random Factor Loading Model)，觀察隨機風險因子負荷模型是否對於定價偏誤較其他模型有所改善，並且比較各模型在最佳化參數與定價時的效率，藉此歸納出較佳的合成型擔保債權憑證定價模型。 / During the mid-1990s, credit-derivatives began to be popular and evolved into credit default swaps (CDS), collateralized debt obligation (CDO), and synthetic collateralized debt obligation (Synthetic CDO). Because of the feature of risk sharing, credit-derivatives became an important part of financial market and played the key role in the financial crisis of 2007. So how to price credit-derivatives is a very important issue. When pricing Synthetic CDO, most people use the one-factor coupla model as the structure of reward function, and suppose the distribution of model is Normal distribution, t- distribution or Normal Inverse Gaussian distribution(NIG). But the volatility smile of implied volatility always causes the pricing inaccurate. For solving the problem, I use the random factor loading model under Normal distribution and NIG distribution in this study to test whether the random factor loading model is better than one-factor coupla model in pricing, and compare the efficience of optimization parameters. In conclusion, I will induct the best model of Synthetic CDO pricing.

信用連結債券的價值主要取決於所連結資產池內的資產違約情況，因此過去有許多文獻在評價時會利用Copula模擬各資產的違約時點，或是用Factor Copula估算他們在各時點下的違約機率。而本研究以Gaussian Factor Copula模型為主軸，對資產池違約機率做估計，以得到連結該資產池的信用連結債券價值。但過去文獻較常以給定參數的方式進行評價，本研究進一步利用市場實際資料估出模型參數並加入產業因子，以期達到符合市場的效果。 本研究利用已知的違約資訊對照模型結果，發現在給定原油價格成長率、產業GDP成長率及CAPM殘差之後，使用Factor Copula模型在資產池小且違約比例過高時容易低估損失，主要原因在於各資產的違約機率並非逼近1。且模型算出的預期損失會隨著距今時間變長而增加，但若資產池實際上沒有更多違約公司，模型的結果就可能會高估損失。而所有的變數又以參考價差對該商品價值的影響最大，因參考價差的數值取決於該公司的信用評等，因此可知信用連結債券價值主要還是與各公司信評有最大相關。 / The value of credit linked notes depends on whether the reference entities in the linked asset pool default or not, so some previous studies used Copula model to simulate the times to default or Factor Copula model to get the default probability. In this paper, with the Gaussian Factor Copula model adopted and industry factors taken into account, the default probability is estimated in order to obtain the value of the credit linked notes. Then, unlike other previous studies using the given parameters, this paper evaluated the parameters by using the model as well as market data, hoping to achieve the goal that results can reflect the real market situation. With real default information compared with the modeling results, three findings can be drawn given the growth rate of oil price, the growth rate of industrial GDP and the residuals of CAPM. First, the loss will be underestimated if the asset pool is small and the default proportion is too high mainly because not all the default probability approximates one. Second, expected default probability will be directly proportional to the time period between the present and the expected moment. So if there are not so many defaulting companies, then the loss might be overestimated. Last, the reference spread has the most impact on the product value among all the variables, and as we know, the reference spread of a company depends on its credit rating. Therefore, compared with other factors, credit rating remains the most essential to credit linked notes.

在市場上最常被用來評價抵押債務債券(Collateralized Debt Obligation, CDO)的分析方法即為應用大樣本同質性資產組合(Large Homogeneous Portfolio, LHP)假設之單因子關聯結構模型(One Factor Copula Model)。由過去文獻指出，自2008年起，抵押債務債券的商品結構已漸漸出現改變，而目前所延伸之各種單因子關聯結構模型在新型商品的評價結果中皆仍有改善空間。 在本文中使用標準化偏斜Student-t分配(Standardized Skew Student-t distribution, SSTD)取代傳統的高斯分配進行抵押債務債券之分券的評價，此分配擁有控制分配偏態與峰態的參數。但是與Student-t分配相同，SSTD同樣不具備穩定的摺積(convolution)性質，因此在評價過程中會額外消耗部分時間。而在實證分析中，以單因子SSTD關聯結構模型評價擔保債務債券新型商品之分券時得到了較佳的結果，並且比單因子高斯關聯結構模型擁有更多參數以符合實際需求。 / The most widely used method for pricing collateralized debt obligation(CDO) is the one factor copula model with Large Homogeneous Portfolio assumption. Based on the literature of discussing, the structure of CDO had been changed gradually since 2008. The effects for pricing new type CDO tranches in the current extended one factor copula models are still improvable. In this article, we substitute the Gaussian distribution with the Standardized Skew Student-t distribution(SSTD) for pricing CDO tranches, and it has the features of heavy-tail and skewness. However, similar to the Student-t distribution, the SSTD is not stable under convolution as well. For this reason, it takes extra time in the pricing process. The empirical analysis shows that the one factor SSTD copula model has a good effect for pricing new type CDO tranches, and furthermore it brings more flexibility to the one factor Gaussian copula model.

根據以往探討評價合成型抵押擔保債務憑證之文獻研究，最廣泛使用的方法應為大樣本一致性資產組合(large homogeneous portfolio portfolio；LHP)假設之單因子常態關聯結構模型來評價，但會因為常態分配的厚尾度及偏斜性造成與市場報價間的差異過大，且會造成相關性微笑曲線現象。故像是Kalemanova et al.在2007年提出之應用LHP假設的單因子Normal Inverse Gaussian(NIG)關聯結構模型以及邱嬿燁(2007)提出NIG及Closed Skew Normal(CSN)複合分配之單因子關聯結構模型(MIX模型)皆是為了改善其在各分劵評價時能達到更佳的評價結果 ，然而過去的文獻在評價合成型抵押擔保債務憑證時，需要將CDS價差、各分劵真實報價之資訊導入模型，並藉由此兩種資訊進而得到相關係數及報價，故靜態模型大多為事後之驗證，在靜態模型方面，我們嘗試使用不同概念之CDS取法以及相對到期日期數遞減之概念來比較此兩種不同方法與原始的關聯結構模型進行比較分析，在動態模型方面，我們應用與時間序列相關之方法套入以往的評價模型，針對不同商品結構的合成型抵押擔保債券評價，並由實證分析來比較此兩種模型，而在最後，我們利用時間序列模型來對各分劵進行預測。

根據以往探討評價合成型抵押擔保債券之文獻研究，最廣為使用的方法應用大樣本一致性資產組合(large homogeneous portfolio portfolio ; LHP)假設之單因子常態關聯結構模型來評價，但會造成合成型抵押擔保債券憑證與市場報價間的差異過大，且會造成相關性微笑曲線現象。由文獻顯示，單因子關聯結構模型若能加入厚尾度或偏斜性能夠改善以上問題，且對於分券評價時也會有較好的效果，像是Kalemanova et al. (2007) 提出應用LHP假設之單因子Normal Inverse Gaussian(NIG)關聯結構模型以及邱嬿燁(2007)提出NIG及Closed Skew Normal(CSN)複合分配之單因子關聯結構模型(MIX模型)在實證分析中得到極佳的評價結果。自2008年起，合成型抵押擔保債券商品結構開始出現變化，而以往評價合成型抵押擔保債券價格時，商品結構皆為同一種型式。本文將利用常態分配、NIG分配、CSN分配以及NIG與CSN複合分配作為不同的單因子關聯結構模型，藉由絕對誤差極小化方法，針對不同商品結構的合成型抵押擔保債券評價，並進行模型比較分析。由最後實證分析結果顯示，單因子NIG(2)關聯結構模型優於其他模型，也證明NIG分配的第二個參數 β 能夠帶來改善的評價效果，此項證明與過去文獻結論有所不同，但 MIX模型則為唯一一個符合LHP假設的模型。 / Based on the literature of discussing the approach for pricing synthetic CDOs, the most widely used methods used application of Large Homogeneous Portfolio (LHP) assumption of the one factor Gaussian copula model, however , it fails to fit the prices of synthetic CDOs tranches and leads to the implied correlation smile. The literature shows that one factor copula model adding the heavy-tail or skew can improve the above problem, and also has a good effect for pricing tranches such as Kalemanova et al (2007) proposed the application of LHP assumption of one factor NIG copula model and Qiu Yan Ye (2007) proposed the application of LHP assumption of one factor NIG and CSN copula model. This article found that the structure of synthetic CDOs began to change since 2008. The past of pricing synthetic CDOs, the structure of synthetic CDOs are the same type, so this article will use different one factor copula model for pricing different structure of synthetic CDOs by using the absolute error minimization. This article will observe whether the above model can be applied in the new synthetic CDOs and implement of different type model for comparative analysis. The last empirical analysis shows that one factor NIG (2) copula model is superior to other models, more meeting the actual market demand, also proving the second parameter β of the NIG distribution able to bring about improvements in pricing results. This proving is different for the past literature conclusions. However, the MIX model is the only one in line with the LHP assumptions.

依據之前的文獻研究，市場上主要是在LHP (Large Homogeneous Portfolio) 假設下利用單因子常態關聯結構模式(One factor double Gaussian copula model) 評價擔保債權憑證 (Collateralized debt obligation, CDO)。但這會造成擔保債權憑證的評價與市場報價的差距過大，且會造成base correlation偏斜的情況。Kalemanova et al. (2007) 提出用Normal inverse Gaussian (NIG) 取代常態分配評價擔保債權憑證，此模型不但計算快速而且可以準確估計權益分券 (equity tranche) 的價格，但是它也過於高估了其它的分券的價格。 在本文中使用多變量封閉常態分配(Closed skew normal, 簡稱CSN) 分配取代NIG分配作擔保債權憑證分券的評價，CSN分配具有常態分配的性質，其線性組合仍具有封閉性的特質，且具有較多的參數以控制分配的偏態與峰態。但是與單因子常態關聯結構模式相同，多變量封閉常態分配的單因子關聯結構模式仍然無法估計的很準確，僅有在最高等級分券(senior tranche)的評價上有明顯的改進。 因此在本文中我們使用NIG與CSN複合分配之單因子關聯結構模式評價擔保債權憑證分券，在實例分析時得到極佳的評價結果，並且比單因子常態關聯結構模型具有更多的的參數以使模型更符合實際的需求。 / This article extends the Large Homogeneous Portfolio (LHP) and one factor double Gaussian copula approach for pricing CDOs. In the literature, the one factor double Gaussian copula model under LHP assumption fails to fit the prices of CDO tranches, moreover, it leads to the implied base correlation skew. Some researchers proposed using one factor double NIG copula model to price CDO tranches. It not only economizes on time but also fits the equity tranches exactly, but NIG models do not price other tranches well simultaneously. On the other hand, we substitute the NIG distribution with the Closed Skew normal (CSN) distribution. This family also has properties similar to the normal distribution, which is closure under convolution, and has extra parameters to control the shape. By using this model we get a better fit in the senior tranches, but it seriously overprices subordinate tranches. Thus we consider a mixture distribution of NIG and CSN distributions. The employments of this mixture distribution are comparatively well, and furthermore it brings more flexibility to the dependence structure.